The aerodynamic drag of high speed trains

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Journal of Wind Engineering and Industrial Aerodynamics, 34 (1990) 273-290 Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands 273 THE AERODYNAMIC DRAG OF HIGH SPEED TRAINS N.J.W. BROCKIE and C.J. BAKER Department of Civil Engineering, Nottingham University~ University Park, Nottingham, NG7 2RD (U.K.) (Received December 15, 1988; accepted in revised'form March 6, 1990) Summary The resistance to forward motion of a high speed passenger train at cruising speed is dominated by aerodynamic drag. To measure train aerodynamic drag a model must be of a small scale in order to fit a standard wind tunnel working section. Due to the scale dependency of the skin friction component of to(~l aerodypAmic drag the results of wind tunnel tests cannot be directly related to train performance at full scale Reynolds number. It is thus necessary to quantify the relat.;enship between skin friction drag and Reynolds number. A series of boundary layer and total aerodynamic drag measurements were made using small scale model high speed passenger trains at zero yaw. Boundary layer measurements were also made at full scale to determine skin friction. A simulation program was used to model the recorded boundary layer development and the train boundary layer was found to be strongly three-dlmen- sional. The dependence of train skin friction drag, and hence the total aerodynamic drag, on Reynolds number was clearly demonstrated but the complexity of the train flow regime at full scale prevented an accurate quantification of this. The nature of the train boundary layer has been clarified and this knowledge will assist future investigations of high speed passenger train aerodynamic drag. Notation a, bbb~C A CDO Cv o Cf Co H k L P R Rek coefficients in train resistance equation train frontal area total aerodynamic drag coefficient at zero yaw pressure drag coefficient local skin friction coefficient skin friction drag coefficient boundary layer velocity profile shape factor yaw correction factor train length train perimeter train total resistance Reynolds number based on train length 0167-6105/90/$03.50 1990--Elsevier Science Publishers S.V. 274 v train velocity relative to the ground V train velocity relative to the ambient wind y coordinate normal to surface Greek letters J* 0 P P zw velocity profile displacement thickness velocity profile momentum thickness kinematic viscosity of air density of air wall shear stress train yaw angle 1. Introduction In recent years there has been increasing pressure for improved performance of high speed passenger trains, whether by increasing fuel efficiency or by in- creasing cruising speeds. To assess the performance of present and future train designs requires that the train resistance be known. This is commonly related to the train speed by the equation: R=a+ bl v+ b2 V' l 'c(~) V 2 (1) Here R is the train total resistance, v is the train velocity relative to the ground, the cvnstants a and bl represent the mechanical resistance effects, the term b2 V corresponds to momentum drag due to infested air, and Vis the train velocity relative to the ambient wind. The term c (~ V 2 is the total aerodyn- amic drag which is a function of the yaw angle, ~P. At train speeds of 250-300 km h- 1 75% of the total resistance to motion is due to aerodynamic drag [ 1 ]. This paper concentrates on high speed passenger train aerodynamic drag. The total aerodynamic drag term in eqn. (1) can be written: C (~/) -- PCDo ( 1 ~- k ~/) where ~P is measured in radians (2) Here A is the train frontal area, CDO is the total aerodynamic drag coefficient at zero yaw, k is the yaw correction factor and p is air density. From classical boundary layer theory is known that the skin friction drag, due to the turbulent boundary layer on a fiat plate, decreases with increasing Reynolds number. By the nature of the large length-to-width ratio of a high speed passenger train skin friction drag is a major component of the total aero- dynamic drag. Thus if the train boundary layer flow can be compared with that of a fiat plate turbulent boundary layer, it is to be expected that the train skin friction will display a Reynolds number dependence between model and full scale. It follows that without correction for Reynolds number effects, model scale wind tunnel results cannot be directly applied at full scale because of the larger skin friction contribution to the total aerodynamic drag at model scale. For high speed passenger train aerodynamic drag, investigations are required to enable the relationship between skin friction drag and Reynolds number to be quantified. 275 The aim of the project reported herein was to establish that relationship by means of model scale tests, full scale tests and computer simulations of mea- sured train boundary layers. Total aerodynamic drag measurements and boundary layer measurements were made on a 1/76th scale HST (British Rail high speed train). Similar measurements were made at 1/40th scale using a different ground effect representation. Boundary layer and skin friction mea- surements were made on a full scale service HST. For greater detail the reader is referred to ref. 2. 2. Experimental method The 1/76th scale tests were performed in the Nottingham University envi- ronmental wind tunnel. An image model technique of ground effect represen- tation was employed with adapted 00-gauge hobbyist models. This technique was chosen, beca-__~ for ~ length trains, if the model is mounted on a f'Lxed ground plane then the ground plane boundary layer growth will submerge the rear part of the train, rendering the model scale skin friction inaccurate. Total aerodynamic drag measurements were made by recording the strain in a ver- tically mounted cantilever as the top train was displaced by the drag load (Fig. 1). Boundary layer measurements were made by hot film anemometry. The 1/40th scale tests were performed in the Southampton University low speed wind tunnel. This has a moving ground belt facility which gives good ground effect representation. The t~in underbody flow and skin friction are accurately modelled for the full length of the train. The train total aerodynamic drag was measured by recording the drag of individual vehicles in the train (Fig. 2). Boundary layer measurements were made by flattened pitot tube trav- erses propelled by a stepper motor located within the model. At full scale a Mk III laboratory coach was inserted into a service HST. Boundary layer measurements were made by projecting a total pressure rake through the coach side as the train travelled along a virtually straight and level length of track (Fig. 3). The rake w~3 limited to 150 mm in length by the British Rail clearance gauge restrictions. Preston tube measurements were also made to assess the feasibility of this method for the measurement of train skin friction st full scale. Experiments were carried out on the straight, level section of the BR East Coast Main Line between York and Northallerton in Northern Flow d,rechon Top trmn \ Track- - / _L ..'r ~ '~Q0e t,.o,, I ! 1 -- ~ r o d _r_ . j . , . ~ . . i / , , I -s'rQ,o g og,d 1 t 1 ~ tl co.t,le,er t V - - -7" Bridge rlrcult balance - ampltflef o~d dtsplny " " Fig. I. 1/76th scale wind tupnel .-~. odeL 276 Foired suspension columns ~/ ' [-'-~ Suspension be,~m Susp( ~ ~ _ Pressure dueling Strain gauge~r~~ t bmann~ meter Loocl measuring DVT ~aessure tapped~BrOU;dory layer Load rneosuring coach Flow direction == ~enslon wires Hoving ground belt Fig. 2.1/40th scale wind tunnel model. Argus Fig. 3. Boundary layer rake and Preston tubes. England. The lab coach was located adjacent to a power car and was the first coach in the rake for southbound runs and the final coach ~vr nc,rthbour~d runs. The ambient wind speed and direction was monitored and virtually still air conditions prevailed during the tests. 3. Results 3.1.1/76th scale A large number of identical tests were performed at 1/76th scale in order that a repeatable mean value of CDO was obtained. This was CDo = 1.85_+ 5% The Reynolds number based on train length was Rej = 2.54 106. 277 Boundary layer mean velocity profiles were measured at sixteen experimen- tal positions on the side and roof of the top train. The mean velocity profile integral parameters are shown in Table 1. The profile positions are identified by the number of the power car (PC) or trailing coach (TC) and a letter F, M or R representing the ~ront, middle or rear respectively of the vehicle side. Figure 4 shows a typical mean velocity profile recorded at position TC4M. At this small scale the first position where a full mean velocity profile could be recorded was at the rear of the leading power car, position PC1R. The devel- opment of the boundary layer along the model was not steady, the profiles recorded at either side of ~he intercoach gaps between coaches I and 2 and TABLE 1 1/76th scale train side boundary layer parameters Position Re, J(m) J*(m) 8(m) H Cf PC1R 1.67 105 0.008 0.0008 0.0015 1.476 TC1F 2.46 105 0.009 0.0014 0.0010 1.454 TCIM 3.78 105 0.010 0.0016 0.0011 1.442 TC 1R 5.01 105 0.020 0.0023 0.0017 1.392 TC2F 5.41X 105 0.018 0.0023 0.0017 1.381 TC2M 6.75 X 105 0.021 0.0028 0.0020 1.381 TC3M 9.72 X 10 ~ 0.026 0.0026 0.0020 1.304 TC3R 1.10X 10 e 0.030 0.0~29 0.0022 1.305 TC4F 1.14 10 s 0.024 0.0627 0.0021 1.262 TC4M 1.27 X 10 s 0.026 0.0029 0.0023 1.277 TC5M 1.57 10 e 0.038 0.0038 0.0030 1.272 TC6M 1.86 10 e 0.037 0.0042 0.0033 1.295 TC7M 2.16 X 10 e 0.035 0.0041 0.0032 1.286 PC2M 2.51 10 s 0.035 0.0032 0.0024 1.338 0.006 0.0045 0.0045 0.0042 0.0042 0.004 0.0042 0.0041 0.0041 0.004 0.0038 0.0037 0.0037 0.0039 10 o sL 0"6" y 5 04- 02. o;2 o.~, o."'e o;e ~.o ulUe Fig, 4. 1/76th scale train side boundary layer velocity profile at TC4M. 278 coaches 3 and 4 show reductions in thickness downstream of the gap. However, the overall behaviour appeared to resemble that of a fiat boundary layer at a similar Reynolds number. The local skin friction coefficient cf was measured at each profile position using the Clauser chart method and this result was checked using the velocity profile expression of Bandyopadhay [3 ] and the skin friction relations in the lag-entrainment method. The cf distribution is also shown in Table 1. The recorded values of cf for the train side were compared with the data of Schlichting [4] for the boundary layer over a sand-roughened fiat plate (Fig. 5). This places the train side boundary layer in the transitionally rough regime between the aerodynamically smooth and ~lly rough states. This agreed with the full scale measurements of Morrow [5 ] and Richards and Cooper [6 ] for a Mk I coach and advanced passenger train respectively. The train roof boundary layer was much more complex than that over the train side. Over the front half of the leading power car, cotton tuft flow visual- isation revealed a degree of divergent flow probably due to the wake shed by the leading bogies and shielding. This washed up over the side of the power car and thickened the roof boundary layer. However over the rear half of the power car this effect appeared to have diminished and more conventional profiles were recorded. From the first coach the train roof boundary layer grew much more rapidly, 1 ! 105 2 5 10 e 2 5 10 ? 2 5 10 e 2 5 109 2 5 U~x v q, Fig. 5. Variation of ct with R% far a rough fiat plate boundary layer: Q, 1/76th scale train side; 0 , 1/76th scale train roof; , 1/40th scale train side; +, full scale train side. 3x~03 lx10 ~ 3xi0/ . lx105 3x10 s Uwk,~ 15 v " , \ \ \ TABLE 2 i/76th scale train roof boundary layer parameters 279 Position Re, J(m) J*(m) 6(m) H c~ RPCIF 4.91 104 0.010 0.0049 0.0015 3.196 - RPC 1M 1.08 105 0.023 0.0053 0.0034 1.534 0.0025 RPCIR 1.67 10 s 0.035 0.0051 0.0041 1.244 0.0037 RTCIF 2.46 10 s 0.028 0.0021 0.0017 L262 0.0045 RTCIM 3.78X10 s 0.011 0.0013 0.0009 1.345 0.0047 RTCIR 5.01 X 105 0.017 0.0016 0.0012 1.363 0.0042 RTC2F 5.41 X 105 0.020 0.0021 0.0014 1.447 0.004 RTC2M 6.72 X 105 0.024 0.0030 0.0022 1.342 0.0035 RTC3M 5.75 X 105 0.040 0.0047 0.0037 1.274 0.0035 RTC3R 1.10 X 105 0.050 0.0062 0.0049 1.262 0.0034 RTC4F 1.14 X 105 0.060 0.0081 0.0065 1.246 0.0032 RTC4M 1.20 X 106 0.060 0.0069 0.0056 1.246 0.0032 RTC5M 1.57 X 105 0.0035 RTC6M 1.86 X 106 0.0037 RTC7M 2.16X 10 e 0.0035 RPC2M 2.51X 106 0.0030 the presence of inter-coach gaps having little apparent effect. At positions downstream of the train mid-point it became too thick for the traverse equip- ment to measure to the boundRry layer edge. The integral parameters and skin friction coefficients are shown in Table 2. The measured values of cf did not compare well with the data of Schlichting, mostly falling below the aerodynamically smooth line (Fig. 5). The train roof was far from a smooth surface. This was the first indication of a departure from the fiat plate boundary layer condition. The 1/76th train skin friction drag was calculated from the above measure- ments. This is defined as: Fo = pV pL where Fo is the skin friction drag force, p is the train perimeter and L is the train length. A value of Cfo- 0.0044 _+ 10% was obtained. 3.2. 1/40th scale The drag measurements reported here were performed by British Rail Re- search Division Aerodynamics Unit. The boundary layer measurements were performed in collaboration with the authors. The total aerodynamic drag coefficient of a 1/40th scale model IC225, which 280 has almost identical geometry to the HST, in a nine vehicle rake was found to be: C~o =1.84+_5% This value compared well with the result at 1/76th scale for a very similar train design. The Reynolds number for the 1/40th scale tests was Rei-- 1.08 107. The number of boundary layer velocity profile measurement positions was limited by the ~odel design to the side mid-point of the first 5 coaches. No train roof profiles were recorded. To reduce the aerodynamic sidt ~ loading on the pitot probe, the freestream velocity was reduced to 20 m s- ~, giving a Ray- nolds number based on train length of Rel = 7.0 10 e. The velocity profile integral parameters and the local skin friction coeffi- cient were evaluated as at 17/6th scale. The results of these measurements are shown in Table 3. As at the smaller scale, an irregular train side boundary layer development was noted but the values of the integral parameters compared reasonably well with those for a fiat plate turbulent boundary layer at a similar Reynolds number. Compared with the data of Schlichting [4 ] in Fig. 5, the values ofcf lay close to the aerodynamically smooth line. Again this is unlikely and suggested a departure from the fiat plate condition. 3.3 Full scale Mean velocity profiles were obtained at four locations on the test track. These all displayed classical turbulent boundary layer form as shown by Fig. 6. The free stream velocity at the boundary layer edge was taken as v, the train speed, since there was little or no crosswind. A value of local skin friction was ob- tained using the Clauser method as before and also from the Preston tube measurements using the calibration of Head and Vasanta Ram [ 7 ]. To obtain some indication of the boundary layer thickness, a curve of the form ~/U-- (y/J) ~/" was fitted through the profile points and this was extrap- olated to a value of u/Uffi 0.99. The integral parameters were also calculated ~n this way by obtaining a power law index n from the curve fitting procedure and inserting this into the definitions. TABLE 3 1/40th scale boundary layer parameter ~ Position Re= J(m) J*(m) e(m) H cf TC 1M 1.05 X 10 e 0.03 0.0047 0.0036 1.307 TC2M 1.86 l0 s 0.053 0.0046 0.0037 1.218 TC3M 2.67 l0 s 0.061 0.0052 0.0043 1.194 TC4M 3.48 10 e 0.085 0.0078 0.0064 1.218 TC5M 4.29 106 0.09 0.0070 0.0057 1.222 0.0033 0.0035 0.0037 0.0034 0.0034 0 200 o 16o o 12C 0 080 I I o 040 i | . ~ m 8~ o2o o~o6o 06 ,oo 281 Fig. 6. Full scale train side boundary layer profde at position TCIM. TABLE 4 Full scale results for boundary layer over leading coach Cn from rough wall method [5] Cn fron~ preston tube Site Re, J(m) J*(m) 0(m) H cn cf2 (a) 1.2 l0 s 1.88 0,182 0,153 1,194 0,0011 (b) 1.2los 2.32 0.226 0.189 1.195 0.0011 (c) 1.2X los 2.14 0,209 0,175 1,196 0.0011 (d) 1.2X los 1.89 0,184 0,154 1,195 0.0013 0.0014 0.0013 0.00135 0.0014 TABLE 5 Full scale results for boundary layer over trailing coach Site Re, J(m) J*(m) 0(m) H cn cn (a) 8.8 los 1.94 0,216 0,176 1,229 0.0013 0.0012 (b) 9.0 los 2.21 0,243 0,198 1.26 0.0013 0.00125 (c) 8.7 l0 s 1.83 0.204 0.166 1.229 0.0013 0.00125 (d) 8.5X l0 s 1.82 0.205 0.166 1.232 0.0013 0.0012 J nJ J*= 0~- (n+l ) (n+l ) (n+2) The integral parameters and local skin friction coefficients for the boundary layer over the leading coach are given in Table 4. Those for the trailing coach are in Table 5. The methmt of extrapolating the boundary layer velocity profile to obtain the boundary layer thicknes~ and the integral parameters was far from ideal but due to the limited nature of the experimental profiles no other means was 282 10 09 08 07 uO.6 U05 04 03 02 01 0 O ....... J . . . . . "J . . . . . . ., . . . . . . j . . . . . . a 0 z 103 10" 10 s 106 107 yU/v +~ Fig. 7. Clauser chart for full scale train side boundary layer profile at position TC1M. available. However, the results showed good self consistency and provided an indication of the disturbed nature of the train side boundary layer at the front of the train. The semi-logarithmic plot of the profile points on the Clauser chart did not concur with the family of lines of constant cf (Fig. 7). The rough wall method of Morrow [5] also failed to produce a realistic value of cf. The Preston tube values were taken as correct. At the rear of the train the boundary layer had relaxed to a more ordered state more closely resembling a flat plate turbulent boundary layer at a similar high Reynolds number. The three methods of skin friction evaluation were in much better agreement. Although the results from the full scale tests were less conclusive than was hoped, some indication was achieved of the nature of the train side boundary layer. Compared with the data of Schlichting [4 ] (Fig. 5) the full scale values ofcf lay well below the aerodynamically smooth line. The full scale service train was far from a smooth body and again the comparison with the fiat plate boundary appeared to be unjustified. 4. Boundary layer prediction The lag-entrainment integral prediction method is based around the concept of equilibrium in boundary layer flows [8]. The program used predicts two- dimensional boundary layer development over a surface specified by the user, and outputs the values of J*, 0, H and cf at each specified surface station. An adapted rough surface model was produced by compensating for roughness effects within the lag-entrainment skin friction roughness Reynolds number, Rk--~ ksU/p, at each surface station. For all the boundary layer simulations the free stream velocity was defined as constant over the surface. 283 4.1.1/76 scale train boundary layer The predicted and measured boundary layer development is shown in Fig. 8. The smooth surfacv predictions are shown. There was good agreement over the first three vehicles but thereafter agreement was reduced. The effects of roughness simulation were found to be minimal. It was apparent that an accurate simulation of the measured train side boundary layer could not be achieved with the strictly two-dimensional model. A momentum balance calculation was performed to assess any possible three- dimensionality of the experimental boundary layer flow. This provided evi- dence of a divergent train side flow with the degree of divergence increasing downstream along the train. A re-examination of the predictions supported this: the measured moment-m thickness growth was less than that predicted for the corresponding two-dimensional bound-ry layer. It was possible to allow for three dimensional effects within the log-entrain- ment program. The experimental momentum thickness distributed is input and computation of a freestream convergence or divergence ensures that the predicted and measured 8 distributions agree exactly. The momentum integral and entrainment equations were amended to include cross flow terms and the predictions of H and cf showed more agreement with experiment. Incomorat- ing an allowance for convergence or divergence produced a much improved 0.005" 0.004- D (m 610.003. O. 002' 0 001, "o's',.b 1.'s '2'o X (m) 0-005 0004- [era] 0.003- 0002- 0.001- f "oL~ " t'o 1.'s 2'.o X (m) 25" 2.0' 1.5' H 1.0' 0-5' 0-007 0006' 0005 O 004" Cf 0- 003- 0002- 0.001" - - . - . , , ! , o'.5 ,Io iis 2'o o's 1o ~15 ~'o X {m] X (m} Fig . 8. Prediction of 1/76th scale train side boundary layer: - - tion with 3D effects allowed for, O, experimental data. ,2D pred ic t ion ; w ____ , predic- 284 0.0101 o.oo81 %- ~" / o (m)0.0061 / / /t~ 2T. ,~ , , , 0 50 100 150 200 X (m) 00101 0 0081 Aooo, t ,o 0002~, i , I " t ~ ' '~ , j . 50 100 150 Xlm} 200 25" 20- 1.5 H 10 05" 0.o07 0 006- 0 005 i 0 O0/.,- Cf 0 003" 0002" 0.001- )\ 1 I 1 I I I 5(} 100 15(3 200 50 1130 150 2(3(} X(m) v t-~ * , L~ l ln Fig. 9. Prediction of 1/76th scale train roof boundary layer (for key, see Fig. 8). prediction of the experimental results with both the smooth and rough surface models as shown in Fig. 8. The two-dimensional lag-entrainment model also faile~ to provide a good prediction of the train roof boundary layer and a convergent train roof flow was deduced from a momentum balance calculation. The agreement between the predicted and experimental flows was improved by the allowance for mo- mentum imbalance within the model. In Fig. 9 the final three experimental points are shown only in the plot of cf distribution because the growth of the train roof bouz;dary layer beyond the upper limit of the traverse equipment rendered the calculation of the integral parameters impossible. The inner part of the velocity profile was however measured and cf could be determined from the Clauser chart. As before there was little difference between the rough and the smooth sur- face simulation. It was apparent that at 1/76th scale a train flow regime existed that was divergent over the train side and convergent over the train roof. These two conditions are compatible and are consistent with a flow regime where the wake from the lower part of the train body washes up the side and over the roof. This seems a physically plausible conjecture. 4.2. 1/40th scale train boundary layer Lag-entrainment simulations were obtained in exactly the same manner as described previously. The comparison between the predicted and measured 0 010 0008- 6e im)O 006: 0 0O4 ~ 0 002. X (m) I /. 0 010 0 008 lm),., ~6 0 004 0 002' ~ J i * , | X(m) 285 25" 20" 15" H 10" 05- ~o o--~-0 X[m) o 005"1 / C 0004-1 o o o _ 00021 00011 , '1 , , , o , , 1 2 3 ~, X {m) Fig. 10. Prediction of 1/40th scale train side boundary layer (for key, see Fig. 8). boundary layer development is shown in Fig. 10. As before, roughness effects were found to be small. From a momentum balance calculation it was concluded that there was a divergent train side flow at 1/40th scale. This was again supported by the two- dimensional log-entrainment simulation that showed the experimental mo- mentum thickness growth was less than for the corresponding two-dimen- sional boundary layer. Incorporating the momentum imbalance routine into the prediction, as described previously, produced improved agreement with the experimental flow (Fig. 10). The agreement between the resets at both model scales, showing a similar train side flow regime led to the deduction of a convergent train roof boundary layer at 1/40th scale. The boundary layer three-dimensionality observed at the smaller scale was not merely a property of the image model technique. Its ex- istence at 1/40th scale, using the mo~ng ground belt technique indicated that it was possibly a genuine tr-in bound,ry layer feature. 4.3. Full scale train boundary layer The predicted full scale boundary layer development from the experimental conditions at the leading coach was compared with the experimental condi- tions at the rear coach (Fig. 11). As before there was very little difference between the smooth and rough surface models. The J* and 8 distributions were 286 0 40' 035" 030- 5 025- Ira) 020" 0-15" 010- 0 05- ~ 0 0 40, o35' 0 30. 0 025- (m) 020- 0 15 .( o~o~ o os: J o s'o ",Go',~o 2oo ~'o "~o ~ 20o Xlrn) X(rnl 200" 1'75- 150" 1 251 H10lY 0 75' 050" 0 25" 30E-4 25E-4 - 20E-4 - CI15E-4 10E-4 5E~4 I 1 ' / ' ~ ! i ! 50 100 150 200 50 100 150 2130 X(m) X Ira) Fig. 11. Prediction of full scale train side boundary layer (for key, see Fig. 8). considerably overpredicted at the ninth coach, resembling the model scale re- sults where a divergent train side flow was deduced. With only two experimen- tal points, a momentum balance calculation was not practical. For the same reason a prediction with an allowance for momentum imbalance was not per- formed. However, some evidence had been obtained that the divergence ob- served at both model scales was also present in the full scale train side bound- ary layer. An extension of this reasoning would suggest that the full scale train roof flow is convergent. The use of the lag-entrainment prediction model was very instructive in highlighting these flow features. However, it was still essentially a two-dimen- sional model and the effect on the train skin friction due to the boundary layer three-dimensionality remained unclear. 5. Train aerodynamic drag The results of an earlier series of tests to investigate the drag of an HST train set were examined [9]. From these a total aerodynamic drag coefficient of CDO = 1.65 _ 15% was established. The uncertainty in the measurements was due to an inherently noisy data collection process and the lack of a correction for crosswind effects. No attempt was made to account for these in the original report and the given error bound of___ 15% is purely an estimate. The above 287 value of Cvo is less than the model scale results reported earlier which corre- sponds with the expected Reynolds number dependent behaviour. The total aerodynamic drag coefficient can be split into a pressure drag com- ponent Cveo and a skin friction drag component Cro [ 10 ]. Cv --CDeo +Cfo(pL/A) where CDeo=Dpo/Jpv2A and Dpo is the pressure drag at zero yaw. The factor pL/A is to standardise the reference areas in eqn. (3). The skin friction coefficient at 1/76th scale was given as Cfo=0.0044. From eqn. 3, the pressure drag coefficient was calculated to be CDeo= 1.10. It was assumed that this was independent of Reynolds number effects and was the same at all scales. To calculate C~ at 1/40th scale the skin friction measurements were com- pared with the results for the whole train at 1/76th scale. Extrapolating from this, a value of C~=0.0039 was obtainecL Using eqn. 3 and the value of CDeo given earlier gave Cvo = 1.84_+ 10% which agreed very well with the total drag coefficient from experiment. The skin friction~ drag of a smooth fiat plate with a boundary layer turbulent from the leading edge is given by the Prandtl-Schlichting relation: 0.455 C/o - loglo(Rei)2.s s (4) As would be expected, eqn. 4 underestimates the calculated skin friction drag of the model scale trains but an expression of similar form might be expected to describe train skin friction drag as a function of Reynolds number, i.e. C~ - ~I (loglo Rel ) -~2 (5) Substituting the model scale values for C~ into eqn. 5 enabled ~1 and a~ to be determined. An estimate of the full scale train skin friction drag was then ob- tained. This was Cm=0.0024. Using eqn. 3 and the value of Cveo obtained ear- lier gave Cvo= 1.47 which is within the error bound of the coastdown test results. From an extrapolation of the predicted full scale train side skin friction sim- ilar to that described earlier a value of C~=0.0017 was obtained. This seemed unrealistically low and when combined with Cveo= 1.10 in eqn. 3 gave a value of Cvo = 1.36 _+ 15%. The error bound of this figure and of the value obtained from the 1984 tests overlapped in the region 1.41 < Cvo < 1.56. Contained within this region is the value of Cvo from the model scale tests and Cm from eqn. 5. A final estimate of the full scale train drag coefficient was obtained by re- casting eqn. 3 into the form: Cfo = (CDo - Cveo)A/pL (6) Substituting for Cvo from the 1984 tests and CDeO from the model scale tests 288 0 005- 000l, 0 003 CF o 0 002 0 001 0 0 o Equat,on 6 0 Equat,on 5 o Extrapolat,on of model results 0 | - -~ 60 70 8'0 9'0 Iogto [Re 1 } Fig. 12. Variation of Cfo with Reynolds number. gave Cfo=0.0036+_ 15%. There is a fairly large degree of uncertainty in this figure owing to the combination of the uncertainties in Cvo and CvPo. Examining all the values obtained for Cm at full scale it seems likely that the actual value will fall within the approximate range 0.002 < Cfo < 0.004. Greater precision than this is not possible without further, more detailed experimental investigation. Accepting this as representative of the range of Cm at full scale gave some indication of the expected Reynolds number dependence of Cm. This is shown in Fig. 12. 6, Conclusions From the work reported herein the following conclusions have been drawn. (i) The total aerodynamic drag coefficient of a 1/76th scale model HST was CDO--1 85+5%. (ii) The skin friction drag coefficient of the same model was Cm = 0.0044 + 6%. (iii) A computer simulation of the train boundary layer at this scale revealed a divergent train side flow and a convergent train roof flow. (iv) The total aerodynamic drag coefficient of a 1/40th scale model IC225 was CDO= 1.84 + 5%. (V) The skin friction drag coefficient of the same model was Cfo = 0.0039 + 10%. (vi) A computer simulation of the train boundary layer at this scale revealed the probability of a similar train flow regime to that at 1/76th scale. (vii) The boundary layer of a full scale HST was shown to have a complex no~a- equilibrium and probably three-dimensional nature. 289 (viii) The expected range of the total aerodynamic drag coefficient for a full scale HST is 1.41 < CDO < 1.56. (ix) The expected range of the skin friction drag coefficient for a full scale HST is approximately 0.002 < Cfo < 0.004. The declared aim of this project was to establish the relationship between skin friction and Reynolds number. This presupposed that the train boundary layer would be adequately represented by a simple two dimensional flow. This has been shown to be an unrealistic simplification. It was demonstrated at two model scales that the train flow regime was substantially three dimensional and it is to be expected that this will be the case at full scale. This knowledge of the nature of train bounda~ layer flows will be a great advantage to future investigations to establish the Cfo-Re relationship more precisely. It has also been demonstrated that unsophisticated, small scale experimen- tal techniques are capable of providing reliable and useful train aerodynamic drag and ~oundary layer information. The image model technique of ground effect representation was shown to be viable for full scale length trains and to agree well with the more widely accepted moving ground technique. Acknowledgements The authors would like to acknowledge the help of British Rail Aerodyn- antics Unit Staff during the course of the project. The first author was sup- ported by ~m S.E.R.C.C.A.S.E. award during the investigation. References I J.L. Peters, Aerodynamics of very high speed trains and maglev vehicles: state of the art and future potential, Int. J. Vehicle Design, Techn. Adv. Vehicle Design Ser. SP3. Impact of Aerodynamics on Vehicle Design, (1983) 308. 2 N.J.W. Brockie, The aerodynamic dragof high speed train, PhD Thesis, Department of Civil Engineeering, Nottingham University, 1988. 3 P.R. Bandyopadlmy, Rough-wall turbulent boundary layers in the transition regime, J. Fluid Mech., 180 (1987)231. 4 H. Sc,~lichting, Boundary Layer Theory, McGraw-Hill, 1968, New York, 6th edn. 5 T.B. Morrow, Turbulent boundary layer measurements on the lateral facesofa railway coach in a t~,~in, Report TT71 R 06, 1971 (Department of Transport Technology, Loughborough University ). 6 S.P. Richards and R.K. Cooper, The measurement ofboundary layer pro/des on TC2 of APT- E and assessment of skin friction, Technical Memorandum TMAERO 23, 1977 (British Rail Research and Development Division, Derby, U.K.). 7 M. Head and V. Vasanta Ram, Simplified p_r~n~tion of Preston tube calibration, Aeronaut. Q., 22 ( i971 ) 295. 8 J.E. Green, D.J. Weeks and J.W.F. Brooman, Prediction of turbulent boundary layers and wakes in compressible flow by a lag-entrainment method, Technical Report 7.o231,1972 ( Royal Aircraft Establishment, Farnborc;,gh, U.K.). 290 9 BR Mechanical and Electrical Engineers, HST tractive resistance tests, BR Testing and Workshops Section Report No. 682, 1964 (Derby, U.K.). 10 C.J. Baker, A critique of the SNCF drag measurements, 1982 (British Rail Research and Development Divizion, Derby. U.K.), unpublished note.

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